Density plot of the expected number of neutrino events (track+cascade) in IceCube for GRB 130427A on the two-dimensional parameter space of the dissipation radius R ₁₃ = R _d /10 ¹³ cm and the bulk Lorentz factor Γ of the jet at this radius. This calculation uses the semi-analytical method similar to Waxman & Bahcall (1997) and Zhang & Kumar (2012) but assuming no specific scenario (e.g., neither an internal shock, nor other model; see Section 2 for details). The blue color (top right region) denotes fewer events while the red (lower regions) denotes more events. The five dashed lines from top to bottom show contours where one event is expected for different proton to electron energy ratios _p / _e = 10, 5, 3, 2, 1. The other two energy partition parameters are taken to be constants, _e = 0.1 and _B = 0.01. Based on the null result in the IceCube neutrino search reported in Abbasi et al. (2012), the parameter space below each contours is more likely to be ruled out for the corresponding _p / _e .